Finite Group Databasebeta

← #14279082

Subgroups — #14279082

Order 1920.

332 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752404C212yesmaximal
2C3×#65399C211yesmaximal, characteristic
3#10598768—31nomaximal, Hall
4C2×C3×#709C2211yescharacteristic
5#91989—22no—
6C22×C3×C5×C8C411yescharacteristic, complemented
7C2×C3×#681C411yescharacteristic, complemented
8#91240C414yescomplemented
9#91228—22no—
10C3×#3952—22no—
11#67691—51nomaximal, Hall
12#65745—32no—
13#65399D311yescharacteristic
14C22×C3×C4×C5C2×C411yescharacteristic
15C2×C3×C22⋊D5C2×C412yes—
16C3×#709—41no—
17C3×#709—41no—
18C2×C3×D20D411yescharacteristic
19C2×C3×C4×D5D412yes—
20C2×C3×Dic10Q811yescharacteristic
21#6763—24no—
22C4⋊ΓL(1,𝔽16)—42no—
23C4×ΓL(1,𝔽16)—42no—
24C2×C3×C5×C8—21no—
25C2×C3×C5×C8—41no—
26C3×#681—41no—
27C2×C3×#168—21no—
28C3×#408—51no—
29#5240—52no—
30C2×#709C2×D311yescharacteristic
31#4130—62no—
32C22×C5×C8Dic311yescharacteristic, complemented
33C2×#681Dic311yescharacteristic, complemented
34#4011—34no—
35#3999—62no—
36#3952—22no—
37#1391—151noSylow
38C23×C3×C5C4211yescharacteristic
39C22×C3×D5C22⋊C412yes—
40C2×ΓL(1,𝔽16)—44no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×C4×C5C4⋊C411yescharacteristic
45C3×C22⋊D5—42no—
46C2×C3×Dic5C4⋊C412yes—
47C3×D20—41no—
48C3×C4×D5—22no—
49C3×C4×D5—22no—
50C3×Dic10—41no—
51C3×C5×C8—41no—
52C3×#168—41no—
53C2×C3×#41—51no—
54C2×C3×M16—51no—
55C22×C3×C8AGL(1,𝔽5)11yescharacteristic, complemented
56#926—102no—
57C3×C22⋊C8—102no—
58#834—54no—
59#834—102no—
60C22×C4×C5C2×Dic311yescharacteristic
61C2×C22⋊D5C4×D312yes—
62#709—41no—
63#709—41no—
64C2×D20D1211yescharacteristic
65C2×C4×D5#6712yes—
66C2×Dic10Dic611yescharacteristic
67C22⋊AGL(1,𝔽5)—64no—
68C4⋊AGL(1,𝔽5)—122no—
69C4×AGL(1,𝔽5)—122no—
70C2×C5×C8—21no—
71C2×C5×C8—41no—
72#681—41no—
73C2×#168—21no—
74#410—152no—
75#408—51no—
76C22×C3×C5—21no—
77C22×C3×C5—41no—
78C22×C3×C5#9511yescharacteristic
79C2×C3×D5—22no—
80C2×C3×D5—42no—
81ΓL(1,𝔽16)—84no—
82C3×C4×C5—21no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#9911yescharacteristic
85C3×Dic5—22no—
86C3×#41—201no—
87C3×#41—201no—
88C2×C3×Q8—51no—
89C2×C3×D4—52no—
90C2×C3×D4—51no—
91C22×C3×C4—52no—
92C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
93C3×M16—201no—
94C2×C3×C8—21no—
95C2×C3×C8—41no—
96C2×C3×C8—101no—
97#217—104no—
98C4⋊Dic3—202no—
99C4×Dic3—202no—
100C23×C5C4×Dic311yescharacteristic
101C22×D5(C2×D3)⋊C412yes—
102C2×AGL(1,𝔽5)—124no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5C4⋊Dic311yescharacteristic
106C2×C4×C5#21711yescharacteristic
107C22⋊D5—42no—
108C2×Dic5Dic3⋊C412yes—
109D20—41no—
110C4×D5—22no—
111C4×D5—22no—
112Dic10—41no—
113C5×C8—41no—
114#168—41no—
115C2×#41—51no—
116C2×M16—51no—
117C22×C8ΓL(1,𝔽16)11yescharacteristic, complemented
118#117—302no—
119#99—154no—
120#99—302no—
121C22⋊C8—102no—
122C2×C3×C5—21no—
123C2×C3×C5—41no—
124C2×C3×C5#34211yescharacteristic
125C3×D5—42no—
126C23×C3—52no—
127C23×C3C4×AGL(1,𝔽5)11yescharacteristic
128C3×Q8—201no—
129C3×D4—201no—
130C3×D4—202no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—52no—
134C2×C3×C4—102no—
135C2×C3×C4—102no—
136C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
137C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
138C2×Dic3—204no—
139C3×C8—41no—
140C3×C8—201no—
141C22×C5—21no—
142C22×C5—41no—
143C22×C5C3⋊#9511yescharacteristic
144C2×D5—22no—
145C2×D5—42no—
146AGL(1,𝔽5)—244no—
147C4×C5—21no—
148C4×C5#83411yescharacteristic
149C4×C5#83411yescharacteristic
150Dic5—22no—
151#41—201no—
152#41—201no—
153C2×Q8—51no—
154C2×D4—52no—
155C2×D4—51no—
156C22×C4—52no—
157C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
158M16—201no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—101no—
162C4⋊C4—602no—
163C22⋊C4—304no—
164C42—602no—
165C3×C5#139111yescharacteristic, complemented, Hall
166C22×C3—21no—
167C22×C3—41no—
168C22×C3—102no—
169C22×C3—202no—
170C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
171C3×C4—21no—
172C3×C4—102no—
173C3×C4#399911yescharacteristic
174C3×C4#401111yescharacteristic
175Dic3—404no—
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#452611yescharacteristic
179D5—42no—
180C23—52no—
181C23C4×ΓL(1,𝔽16)11yescharacteristic
182Q8—201no—
183D4—201no—
184D4—202no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—52no—
188C2×C4—102no—
189C2×C4—102no—
190C2×C4—604no—
191C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
192C2×C4#676311yescharacteristic
193C8—41no—
194C8—201no—
195C2×C3—21no—
196C2×C3—41no—
197C2×C3—202no—
198C2×C3#6491711yescharacteristic
199C5#6769111yescharacteristic, complemented, Sylow
200C22—21no—
201C22—41no—
202C22—102no—
203C22—202no—
204C22#9123511yescharacteristic
205C4—21no—
206C4—102no—
207C4—1204no—
208C4#9122811yescharacteristic
209C4#9124011yescharacteristic
210C3#1059876811yescharacteristic, complemented, Sylow
211C2—21no—
212C2—41no—
213C2—202no—
214C2#1174678811yescharacteristic
subgroupG/H
centerC4#91240
commutatorC23×C3×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC2×C3×C5#342
prime radical, cosocleC2×C3×#709C22
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5#1391
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. C22×C3×C5×C8C4semidirect
7. C2×C3×#681C4semidirect
8. #91240C4semidirect
32. C22×C5×C8Dic3semidirect
33. C2×#681Dic3semidirect
55. C22×C3×C8AGL(1,𝔽5)semidirect
117. C22×C8ΓL(1,𝔽16)semidirect
165. C3×C5#1391semidirect
199. C5#67691semidirect
210. C3#10598768semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117524042
C3×#653992
#105987683
#676915